Complex Power Flow in Single Phase Load to Three Phase Load

Complex Power Flow in Single Phase Load to Three Phase Load:

Now we are going to discuss about Complex Power Flow in Single Phase Load to Three Phase Load. Let us see one by one.

Consider a Complex Power Flow in Single Phase Load fed from a source as in Fig. 4.9. Let

Complex Power Flow in Single Phase Load to Three Phase Load

When θ  is positive, the current lags behind voltage. This is a convenient choice of sign of θ in power systems where loads have mostly lagging power factors.

Complex power flow in the direction of current indicated is given by

Here

  • S = complex power (VA, kVA, MVA)
  • |S| = apparent power (VA, kVA, MVA); it signifies rating of equipment’s (generators, transformers)

P = |V| |I| cos θ = real (active) power (watts, kW, MW)

Q= |V| |I| sin θ = reactive power

= voltamperes reactive (VAR)

= kilovoltamperes reactive (kVAR)

= megavoltamperes reactive (MVAR)

It immediately follows from Eq. (4.17) that Q, the reactive power, is positive for lagging current (lagging power factor load) and negative for leading current (leading power factor load). With the direction of current indicated in Fig. 4.9, S = P + jQ is supplied by the source and is absorbed by the load.

Equation (4.17) can be represented by the phasor diagram of Fig. 4.10 where

Complex Power Flow in Single Phase Load to Three Phase Load

If two (or more) loads are in parallel as in Fig. 4.11

Complex Power Flow in Single Phase Load to Three Phase Load

As per Eq. (4.19), Kirchhoff’s current law applies to complex power (also applies separately to real and reactive powers).

In a series RL load carrying current I,

In case of a series RC load carrying current I,

Consider now a balanced three-phase load represented in the form of an equivalent star as shown in Fig. 4.12. The three phase complex power fed into load is given by

Complex Power Flow in Single Phase Load to Three Phase Load

Here

If VL, the line voltage, is expressed in kV; and IL, the line current in amperes, S is in kVA; and if the line current is in kiloamperes, S is in MVA.

In terms of load impedance Z,

Complex Power Flow in Single Phase Load to Three Phase Load

Substituting for IL in Eq. (4.20)

Complex Power Flow in Single Phase Load to Three Phase Load

If VL, is in kV, S is now given in MVA. Load impedance Z if required can be calculated from

Complex Power Flow in Single Phase Load to Three Phase Load

Updated: April 13, 2020 — 4:43 pm